(* Content-type: application/vnd.wolfram.mathematica *)

(*** Wolfram Notebook File ***)
(* http://www.wolfram.com/nb *)

(* CreatedBy='Mathematica 10.4' *)

(*CacheID: 234*)
(* Internal cache information:
NotebookFileLineBreakTest
NotebookFileLineBreakTest
NotebookDataPosition[       158,          7]
NotebookDataLength[     67032,       2115]
NotebookOptionsPosition[     62075,       1952]
NotebookOutlinePosition[     64772,       2031]
CellTagsIndexPosition[     64627,       2024]
WindowTitle->TID
WindowFrame->Normal*)

(* Beginning of Notebook Content *)
Notebook[{
Cell[BoxData[GridBox[{
   {Cell["FEYN CALC SYMBOL", "PacletNameCell"], Cell[TextData[{
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "See Also",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"See Also", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"OneLoopSimplify\"\>":>
       Documentation`HelpLookup[
       "paclet:FeynCalc/ref/OneLoopSimplify"], "\<\"TIDL\"\>":>
       Documentation`HelpLookup["paclet:FeynCalc/ref/TIDL"]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"SeeAlso"]],
      LineSpacing->{1.4, 0}],
     "\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\[ThickSpace]\
\[ThickSpace]",
     Cell[BoxData[
      ActionMenuBox[
       FrameBox[
        InterpretationBox[Cell[TextData[{
          "URL",
          StyleBox[" \[FilledDownTriangle]", "AnchorBarArrow",
           StripOnInput->False]
         }]],
         TextCell[
          Row[{"URL", 
            Style[" \[FilledDownTriangle]", "AnchorBarArrow"]}]]],
        StripOnInput->False], {"\<\"FeynCalc/ref/TID\"\>":>
       None, "\<\"Copy Wolfram Documentation Center URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell["FeynCalc/ref/TID"]}, Visible -> False]]; 
        SelectionMove[DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; Null], 
       Delimiter, "\<\"Copy web URL\"\>":>
       Module[{DocumentationSearch`Private`nb$}, 
        DocumentationSearch`Private`nb$ = NotebookPut[
           Notebook[{
             Cell[
              BoxData[
               MakeBoxes[
                Hyperlink[
                
                "http://reference.wolfram.com/language/FeynCalc/ref/TID.html"]\
, StandardForm]], "Input", TextClipboardType -> "PlainText"]}, Visible -> 
            False]]; SelectionMove[
         DocumentationSearch`Private`nb$, All, Notebook]; 
        FrontEndTokenExecute[DocumentationSearch`Private`nb$, "Copy"]; 
        NotebookClose[DocumentationSearch`Private`nb$]; 
        Null], "\<\"Go to web URL\"\>":>FrontEndExecute[{
         NotebookLocate[{
           URL[
            StringJoin[
             If[
              TrueQ[DocumentationBuild`Make`Private`wsmlinkQ$269166], 
              "http://reference.wolfram.com/system-modeler/", 
              "http://reference.wolfram.com/language/"], "FeynCalc/ref/TID", 
             ".html"]], None}]}]},
       Appearance->None,
       MenuAppearance->Automatic,
       MenuStyle->"URLMenu"]],
      LineSpacing->{1.4, 0}]
    }], "AnchorBar"]}
  }]], "AnchorBarGrid",
 GridBoxOptions->{GridBoxItemSize->{"Columns" -> {
     Scaled[0.65], {
      Scaled[0.34]}}, "ColumnsIndexed" -> {}, "Rows" -> {{1.}}, 
   "RowsIndexed" -> {}}},
 CellID->1],

Cell[TextData[{
 Cell["TID", "ObjectName"],
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{8, 0}],
    CacheGraphics->False],
   Spacer[8]]]],
 Cell[BoxData[""], "ObjectNameTranslation"]
}], "ObjectNameGrid"],

Cell[CellGroupData[{

Cell[BoxData[GridBox[{
   {"", Cell[TextData[{
     Cell[BoxData[
      RowBox[{"TID", "[", 
       RowBox[{"amp", ",", "q"}], "]"}]], "InlineFormula"],
     " \[LineSeparator]performs  tensor decomposition of 1-loop integrals \
with loop momentum q"
    }]]}
  }]], "Usage",
 GridBoxOptions->{
 GridBoxBackground->{
  "Columns" -> {{None}}, "ColumnsIndexed" -> {}, "Rows" -> {{None}}, 
   "RowsIndexed" -> {}}},
 CellID->982511436],

Cell[CellGroupData[{

Cell[TextData[Cell[BoxData[
 ButtonBox[Cell[TextData[{
   Cell[BoxData[
    InterpretationBox[
     StyleBox[
      GraphicsBox[{},
       BaselinePosition->Baseline,
       ImageSize->{6, 0}],
      CacheGraphics->False],
     Spacer[6]]]],
   "Details"
  }], "NotesFrameText"],
  Appearance->{Automatic, None},
  BaseStyle->None,
  ButtonFunction:>(FrontEndExecute[{
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], All, ButtonCell], 
     FrontEndToken["OpenCloseGroup"], 
     FrontEnd`SelectionMove[
      FrontEnd`SelectedNotebook[], After, CellContents]}]& ),
  Evaluator->None,
  Method->"Preemptive"]]]], "NotesSection",
 WholeCellGroupOpener->True,
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->966192456],

Cell["", "SectionHeaderSpacer"],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"Options", "[", "TID", "]"}]], "Input",
 CellTags->"TID",
 CellLabel->"In[26]:=",
 CellID->1576573941],

Cell[BoxData[
 FormBox[
  RowBox[{"{", 
   RowBox[{
    RowBox[{"ApartFF", "\[Rule]", "True"}], ",", 
    RowBox[{"Check", "\[Rule]", "True"}], ",", 
    RowBox[{"Collecting", "\[Rule]", "True"}], ",", 
    RowBox[{"Contract", "\[Rule]", "True"}], ",", 
    RowBox[{"Dimension", "\[Rule]", "D"}], ",", 
    RowBox[{"DiracSimplify", "\[Rule]", "True"}], ",", 
    RowBox[{"DiracTrace", "\[Rule]", "True"}], ",", 
    RowBox[{"EpsEvaluate", "\[Rule]", "True"}], ",", 
    RowBox[{"ExpandScalarProduct", "\[Rule]", "True"}], ",", 
    RowBox[{"FeynCalcExternal", "\[Rule]", "False"}], ",", 
    RowBox[{"FeynCalcInternal", "\[Rule]", "False"}], ",", 
    RowBox[{"FCLoopRemoveNegativePropagatorPowers", "\[Rule]", "True"}], ",", 
    
    RowBox[{"FCLoopMixedToCartesianAndTemporal", "\[Rule]", "True"}], ",", 
    RowBox[{"FCVerbose", "\[Rule]", "False"}], ",", 
    RowBox[{"FeynAmpDenominatorSimplify", "\[Rule]", "True"}], ",", 
    RowBox[{"Factoring", "\[Rule]", 
     RowBox[{"{", 
      RowBox[{"Factor2", ",", "5000"}], "}"}]}], ",", 
    RowBox[{"FeynAmpDenominatorCombine", "\[Rule]", "True"}], ",", 
    RowBox[{"GenPaVe", "\[Rule]", "False"}], ",", 
    RowBox[{"Isolate", "\[Rule]", "False"}], ",", 
    RowBox[{"PaVeAutoOrder", "\[Rule]", "True"}], ",", 
    RowBox[{"PaVeAutoReduce", "\[Rule]", "True"}], ",", 
    RowBox[{"PauliTrick", "\[Rule]", "True"}], ",", 
    RowBox[{"ToPaVe", "\[Rule]", "False"}], ",", 
    RowBox[{"UsePaVeBasis", "\[Rule]", "False"}], ",", 
    RowBox[{"TimeConstrained", "\[Rule]", "3"}]}], "}"}], 
  TraditionalForm]], "Output",
 ImageSize->{471, 167},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"TID",
 CellLabel->"Out[26]="]
}, Open  ]]
}, Closed]]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "PrimaryExamplesSection",
 WholeCellGroupOpener->True,
 CellTags->"PrimaryExamplesSection",
 CellID->1313542478],

Cell[CellGroupData[{

Cell[TextData[{
 "Basic Examples",
 "\[NonBreakingSpace]\[NonBreakingSpace]",
 Cell["(1)", "ExampleCount"]
}], "ExampleSection", "ExampleSection",
 WholeCellGroupOpener->True,
 CellID->1811038592],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"FCClearScalarProducts", "[", "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{"int", "=", 
  RowBox[{
   RowBox[{
    RowBox[{"FAD", "[", 
     RowBox[{
      RowBox[{"{", 
       RowBox[{"k", ",", "m"}], "}"}], ",", " ", 
      RowBox[{"k", " ", "-", " ", 
       SubscriptBox["p", "1"]}], ",", " ", 
      RowBox[{"k", " ", "-", " ", 
       SubscriptBox["p", "2"]}]}], "]"}], 
    RowBox[{"FVD", "[", 
     RowBox[{"k", ",", "\[Mu]"}], "]"}]}], "//", "FCI"}]}]}], "Input",
 CellTags->"TID",
 CellLabel->"In[1]:=",
 CellID->1762979144],

Cell[BoxData[
 FormBox[
  FractionBox[
   FormBox[
    SuperscriptBox[
     FormBox[
      FormBox["k",
       TraditionalForm],
      TraditionalForm], 
     FormBox[
      FormBox[
       FormBox["\[Mu]",
        TraditionalForm],
       TraditionalForm],
      TraditionalForm]],
    TraditionalForm], 
   RowBox[{
    RowBox[{"(", 
     RowBox[{
      SuperscriptBox[
       FormBox["k",
        TraditionalForm], "2"], "-", 
      SuperscriptBox["m", "2"]}], ")"}], ".", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       FormBox["k",
        TraditionalForm], "-", 
       SubscriptBox[
        FormBox[
         FormBox["p",
          TraditionalForm],
         TraditionalForm], 
        FormBox["1",
         TraditionalForm]]}], ")"}], "2"], ".", 
    SuperscriptBox[
     RowBox[{"(", 
      RowBox[{
       FormBox["k",
        TraditionalForm], "-", 
       SubscriptBox[
        FormBox[
         FormBox["p",
          TraditionalForm],
         TraditionalForm], 
        FormBox["2",
         TraditionalForm]]}], ")"}], "2"]}]], TraditionalForm]], "Output",
 ImageSize->{218, 45},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"TID",
 CellLabel->"Out[1]=",
 CellID->618277373]
}, Open  ]],

Cell[TextData[{
 "By default, all the tensor integrals are reduced to the Passarino-Veltman \
scalar integrals ",
 Cell[BoxData[
  SubscriptBox["A", "0"]], "InlineFormula"],
 ", ",
 Cell[BoxData[
  SubscriptBox["B", "0"]], "InlineFormula"],
 ", ",
 Cell[BoxData[
  SubscriptBox["C", "0"]], "InlineFormula"],
 ", ",
 Cell[BoxData[
  SubscriptBox["D", "0"]], "InlineFormula"],
 " etc. "
}], "Notes",
 CellID->538152640],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TID", "[", 
  RowBox[{"int", ",", "k"}], "]"}]], "Input",
 CellLabel->"In[2]:=",
 CellID->972857906],

Cell[BoxData[
 GraphicsBox[
  TagBox[RasterBox[CompressedData["
1:eJztnXlUVEfa8JPv+yczx5N1nGHGFURAUQx0MoJG1KjRuBHRvFEjnIND4utG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    "], {{0, 225}, {426, 0}}, {0, 255},
    ColorFunction->RGBColor],
   BoxForm`ImageTag["Byte", ColorSpace -> "RGB", Interleaving -> True],
   Selectable->False],
  DefaultBaseStyle->"ImageGraphics",
  ImageSize->Automatic,
  ImageSizeRaw->{426, 225},
  PlotRange->{{0, 426}, {0, 225}}]], "Output",
 ImageSize->{430, 225},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"RasterizedOutput",
 CellLabel->"Out[2]=",
 CellID->1847354466]
}, Open  ]],

Cell[TextData[{
 "Scalar integrals can be converted to the Passarino-Veltman notation via the \
option ",
 StyleBox["ToPaVe", "ExampleText"]
}], "Notes",
 CellID->1396066519],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TID", "[", 
  RowBox[{"int", ",", "k", ",", 
   RowBox[{"ToPaVe", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellLabel->"In[3]:=",
 CellID->1927433685],

Cell[BoxData[
 FormBox[
  RowBox[{
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["1",
            TraditionalForm]],
          TraditionalForm], "2"], " ", 
        FormBox[
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], 
          FormBox[
           FormBox[
            FormBox["\[Mu]",
             TraditionalForm],
            TraditionalForm],
           TraditionalForm]],
         TraditionalForm]}], "-", 
       RowBox[{
        FormBox[
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], 
          FormBox[
           FormBox[
            FormBox["\[Mu]",
             TraditionalForm],
            TraditionalForm],
           TraditionalForm]],
         TraditionalForm], " ", 
        RowBox[{"(", 
         RowBox[{
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], 
          FormBox["\<\"\[CenterDot]\"\>",
           TraditionalForm], 
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm]}], ")"}]}]}], ")"}], " ", 
     FormBox[
      TagBox[
       FormBox[
        RowBox[{
         SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", 
         RowBox[{
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], "2"], ",", "0", ",", 
          SuperscriptBox["m", "2"]}], ")"}],
        TraditionalForm],
       HoldForm],
      TraditionalForm]}], 
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox[
        RowBox[{
         FormBox["\<\"(\"\>",
          TraditionalForm], 
         FormBox[
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}],
          TraditionalForm], 
         FormBox["\<\")\"\>",
          TraditionalForm]}], "2"], "-", 
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["1",
            TraditionalForm]],
          TraditionalForm], "2"], " ", 
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["2",
            TraditionalForm]],
          TraditionalForm], "2"]}]}], ")"}]}]], "-", 
   FractionBox[
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     RowBox[{"(", 
      RowBox[{
       RowBox[{
        FormBox[
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], 
          FormBox[
           FormBox[
            FormBox["\[Mu]",
             TraditionalForm],
            TraditionalForm],
           TraditionalForm]],
         TraditionalForm], " ", 
        RowBox[{"(", 
         RowBox[{
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], 
          FormBox["\<\"\[CenterDot]\"\>",
           TraditionalForm], 
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm]}], ")"}]}], "-", 
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["2",
            TraditionalForm]],
          TraditionalForm], "2"], " ", 
        FormBox[
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], 
          FormBox[
           FormBox[
            FormBox["\[Mu]",
             TraditionalForm],
            TraditionalForm],
           TraditionalForm]],
         TraditionalForm]}]}], ")"}], " ", 
     FormBox[
      TagBox[
       FormBox[
        RowBox[{
         SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", 
         RowBox[{
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm], "2"], ",", "0", ",", 
          SuperscriptBox["m", "2"]}], ")"}],
        TraditionalForm],
       HoldForm],
      TraditionalForm]}], 
    RowBox[{"2", " ", 
     RowBox[{"(", 
      RowBox[{
       SuperscriptBox[
        RowBox[{
         FormBox["\<\"(\"\>",
          TraditionalForm], 
         FormBox[
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}],
          TraditionalForm], 
         FormBox["\<\")\"\>",
          TraditionalForm]}], "2"], "-", 
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["1",
            TraditionalForm]],
          TraditionalForm], "2"], " ", 
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["2",
            TraditionalForm]],
          TraditionalForm], "2"]}]}], ")"}]}]], "-", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"\[ImaginaryI]", " ", 
      SuperscriptBox["\[Pi]", "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm]}], "+", 
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm]}], "-", 
        RowBox[{
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm], " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}], ")"}]}], "-", 
        RowBox[{
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm], " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}], ")"}]}]}], ")"}], " ", 
      FormBox[
       TagBox[
        FormBox[
         RowBox[{
          SubscriptBox["\<\"B\"\>", "\<\"0\"\>"], "(", 
          RowBox[{
           RowBox[{
            SuperscriptBox[
             FormBox[
              SubscriptBox[
               FormBox[
                FormBox["p",
                 TraditionalForm],
                TraditionalForm], 
               FormBox["1",
                TraditionalForm]],
              TraditionalForm], "2"], "-", 
            RowBox[{"2", " ", 
             RowBox[{"(", 
              RowBox[{
               FormBox[
                SubscriptBox[
                 FormBox[
                  FormBox["p",
                   TraditionalForm],
                  TraditionalForm], 
                 FormBox["1",
                  TraditionalForm]],
                TraditionalForm], 
               FormBox["\<\"\[CenterDot]\"\>",
                TraditionalForm], 
               FormBox[
                SubscriptBox[
                 FormBox[
                  FormBox["p",
                   TraditionalForm],
                  TraditionalForm], 
                 FormBox["2",
                  TraditionalForm]],
                TraditionalForm]}], ")"}]}], "+", 
            SuperscriptBox[
             FormBox[
              SubscriptBox[
               FormBox[
                FormBox["p",
                 TraditionalForm],
                TraditionalForm], 
               FormBox["2",
                TraditionalForm]],
              TraditionalForm], "2"]}], ",", "0", ",", "0"}], ")"}],
         TraditionalForm],
        HoldForm],
       TraditionalForm]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        SuperscriptBox[
         RowBox[{
          FormBox["\<\"(\"\>",
           TraditionalForm], 
          FormBox[
           RowBox[{
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], 
            FormBox["\<\"\[CenterDot]\"\>",
             TraditionalForm], 
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm]}],
           TraditionalForm], 
          FormBox["\<\")\"\>",
           TraditionalForm]}], "2"], "-", 
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], "2"]}]}], ")"}]}], ")"}]}], "-", 
   RowBox[{
    RowBox[{"(", 
     RowBox[{"\[ImaginaryI]", " ", 
      SuperscriptBox["\[Pi]", "2"], " ", 
      RowBox[{"(", 
       RowBox[{
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["m", "2"], "+", 
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], "2"]}], ")"}], " ", 
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm]}], "+", 
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["m", "2"], "+", 
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm], "2"]}], ")"}], " ", 
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm]}], "+", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["m", "2"], "+", 
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], "2"]}], ")"}], " ", 
         RowBox[{"(", 
          RowBox[{"-", 
           FormBox[
            SuperscriptBox[
             FormBox[
              SubscriptBox[
               FormBox[
                FormBox["p",
                 TraditionalForm],
                TraditionalForm], 
               FormBox["2",
                TraditionalForm]],
              TraditionalForm], 
             FormBox[
              FormBox[
               FormBox["\[Mu]",
                TraditionalForm],
               TraditionalForm],
              TraditionalForm]],
            TraditionalForm]}], ")"}], " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}], ")"}]}], "-", 
        RowBox[{
         RowBox[{"(", 
          RowBox[{
           SuperscriptBox["m", "2"], "+", 
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm], "2"]}], ")"}], " ", 
         FormBox[
          SuperscriptBox[
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox[
            FormBox[
             FormBox["\[Mu]",
              TraditionalForm],
             TraditionalForm],
            TraditionalForm]],
          TraditionalForm], " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}], ")"}]}]}], ")"}], " ", 
      FormBox[
       TagBox[
        FormBox[
         RowBox[{
          SubscriptBox["\<\"C\"\>", "\<\"0\"\>"], "(", 
          RowBox[{
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], "2"], ",", 
           SuperscriptBox[
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm], "2"], ",", 
           RowBox[{
            SuperscriptBox[
             FormBox[
              SubscriptBox[
               FormBox[
                FormBox["p",
                 TraditionalForm],
                TraditionalForm], 
               FormBox["1",
                TraditionalForm]],
              TraditionalForm], "2"], "-", 
            RowBox[{"2", " ", 
             RowBox[{"(", 
              RowBox[{
               FormBox[
                SubscriptBox[
                 FormBox[
                  FormBox["p",
                   TraditionalForm],
                  TraditionalForm], 
                 FormBox["1",
                  TraditionalForm]],
                TraditionalForm], 
               FormBox["\<\"\[CenterDot]\"\>",
                TraditionalForm], 
               FormBox[
                SubscriptBox[
                 FormBox[
                  FormBox["p",
                   TraditionalForm],
                  TraditionalForm], 
                 FormBox["2",
                  TraditionalForm]],
                TraditionalForm]}], ")"}]}], "+", 
            SuperscriptBox[
             FormBox[
              SubscriptBox[
               FormBox[
                FormBox["p",
                 TraditionalForm],
                TraditionalForm], 
               FormBox["2",
                TraditionalForm]],
              TraditionalForm], "2"]}], ",", "0", ",", 
           SuperscriptBox["m", "2"], ",", "0"}], ")"}],
         TraditionalForm],
        HoldForm],
       TraditionalForm]}], ")"}], "/", 
    RowBox[{"(", 
     RowBox[{"2", " ", 
      RowBox[{"(", 
       RowBox[{
        SuperscriptBox[
         RowBox[{
          FormBox["\<\"(\"\>",
           TraditionalForm], 
          FormBox[
           RowBox[{
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], 
            FormBox["\<\"\[CenterDot]\"\>",
             TraditionalForm], 
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm]}],
           TraditionalForm], 
          FormBox["\<\")\"\>",
           TraditionalForm]}], "2"], "-", 
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], "2"], " ", 
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], "2"]}]}], ")"}]}], ")"}]}]}], 
  TraditionalForm]], "Output",
 ImageSize->{554, 227},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[3]=",
 CellID->1959355442]
}, Open  ]],

Cell[TextData[{
 "We can force the reduction algorithm to use Passarino-Veltman coefficient \
functions via the option ",
 StyleBox["UsePaVeBasis", "ExampleText"]
}], "Notes",
 CellID->709228680],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TID", "[", 
  RowBox[{"int", ",", "k", ",", 
   RowBox[{"UsePaVeBasis", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellTags->"TID",
 CellLabel->"In[4]:=",
 CellID->1686437767],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     FormBox[
      SuperscriptBox[
       FormBox[
        SubscriptBox[
         FormBox[
          FormBox["p",
           TraditionalForm],
          TraditionalForm], 
         FormBox["1",
          TraditionalForm]],
        TraditionalForm], 
       FormBox[
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], " ", 
     FormBox[
      RowBox[{
       SubscriptBox["\<\"C\"\>", "\<\"1\"\>"], "(", 
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["1",
            TraditionalForm]],
          TraditionalForm], "2"], ",", 
        RowBox[{
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["1",
             TraditionalForm]],
           TraditionalForm], "2"], "+", 
         SuperscriptBox[
          FormBox[
           SubscriptBox[
            FormBox[
             FormBox["p",
              TraditionalForm],
             TraditionalForm], 
            FormBox["2",
             TraditionalForm]],
           TraditionalForm], "2"], "-", 
         RowBox[{"2", " ", 
          RowBox[{"(", 
           RowBox[{
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["1",
               TraditionalForm]],
             TraditionalForm], 
            FormBox["\<\"\[CenterDot]\"\>",
             TraditionalForm], 
            FormBox[
             SubscriptBox[
              FormBox[
               FormBox["p",
                TraditionalForm],
               TraditionalForm], 
              FormBox["2",
               TraditionalForm]],
             TraditionalForm]}], ")"}]}]}], ",", 
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["2",
            TraditionalForm]],
          TraditionalForm], "2"], ",", 
        SuperscriptBox["m", "2"], ",", "0", ",", "0"}], ")"}],
      TraditionalForm]}]}], "-", 
   RowBox[{"\[ImaginaryI]", " ", 
    SuperscriptBox["\[Pi]", "2"], " ", 
    FormBox[
     SuperscriptBox[
      FormBox[
       SubscriptBox[
        FormBox[
         FormBox["p",
          TraditionalForm],
         TraditionalForm], 
        FormBox["2",
         TraditionalForm]],
       TraditionalForm], 
      FormBox[
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm],
       TraditionalForm]],
     TraditionalForm], " ", 
    FormBox[
     RowBox[{
      SubscriptBox["\<\"C\"\>", "\<\"2\"\>"], "(", 
      RowBox[{
       SuperscriptBox[
        FormBox[
         SubscriptBox[
          FormBox[
           FormBox["p",
            TraditionalForm],
           TraditionalForm], 
          FormBox["1",
           TraditionalForm]],
         TraditionalForm], "2"], ",", 
       RowBox[{
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["1",
            TraditionalForm]],
          TraditionalForm], "2"], "+", 
        SuperscriptBox[
         FormBox[
          SubscriptBox[
           FormBox[
            FormBox["p",
             TraditionalForm],
            TraditionalForm], 
           FormBox["2",
            TraditionalForm]],
          TraditionalForm], "2"], "-", 
        RowBox[{"2", " ", 
         RowBox[{"(", 
          RowBox[{
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["1",
              TraditionalForm]],
            TraditionalForm], 
           FormBox["\<\"\[CenterDot]\"\>",
            TraditionalForm], 
           FormBox[
            SubscriptBox[
             FormBox[
              FormBox["p",
               TraditionalForm],
              TraditionalForm], 
             FormBox["2",
              TraditionalForm]],
            TraditionalForm]}], ")"}]}]}], ",", 
       SuperscriptBox[
        FormBox[
         SubscriptBox[
          FormBox[
           FormBox["p",
            TraditionalForm],
           TraditionalForm], 
          FormBox["2",
           TraditionalForm]],
         TraditionalForm], "2"], ",", 
       SuperscriptBox["m", "2"], ",", "0", ",", "0"}], ")"}],
     TraditionalForm]}]}], TraditionalForm]], "Output",
 ImageSize->{401, 45},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellTags->"TID",
 CellLabel->"Out[4]=",
 CellID->2009295439]
}, Open  ]],

Cell["\<\
The basis of Passarino-Veltman coefficient functions is used automatically if \
there are zero Gram determinants\
\>", "Notes",
 CellID->933246479],

Cell[CellGroupData[{

Cell[BoxData[{
 RowBox[{
  RowBox[{"FCClearScalarProducts", "[", "]"}], ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"SPD", "[", 
    RowBox[{
     SubscriptBox["p", "1"], ",", 
     SubscriptBox["p", "1"]}], "]"}], "=", "0"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"SPD", "[", 
    RowBox[{
     SubscriptBox["p", "2"], ",", 
     SubscriptBox["p", "2"]}], "]"}], "=", "0"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{
  RowBox[{
   RowBox[{"SPD", "[", 
    RowBox[{
     SubscriptBox["p", "1"], ",", 
     SubscriptBox["p", "2"]}], "]"}], "=", "0"}], 
  ";"}], "\[IndentingNewLine]", 
 RowBox[{"TID", "[", 
  RowBox[{"int", ",", "k"}], "]"}]}], "Input",
 CellLabel->"In[5]:=",
 CellID->1842388488],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", "\[ImaginaryI]"}], " ", 
   SuperscriptBox["\[Pi]", "2"], " ", 
   RowBox[{"(", 
    RowBox[{
     FormBox[
      SuperscriptBox[
       FormBox[
        SubscriptBox[
         FormBox[
          FormBox["p",
           TraditionalForm],
          TraditionalForm], 
         FormBox["1",
          TraditionalForm]],
        TraditionalForm], 
       FormBox[
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], "+", 
     FormBox[
      SuperscriptBox[
       FormBox[
        SubscriptBox[
         FormBox[
          FormBox["p",
           TraditionalForm],
          TraditionalForm], 
         FormBox["2",
          TraditionalForm]],
        TraditionalForm], 
       FormBox[
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm]}], ")"}], " ", 
   FormBox[
    RowBox[{
     SubscriptBox["\<\"C\"\>", "\<\"1\"\>"], "(", 
     RowBox[{"0", ",", "0", ",", "0", ",", 
      SuperscriptBox["m", "2"], ",", "0", ",", "0"}], ")"}],
    TraditionalForm]}], TraditionalForm]], "Output",
 ImageSize->{272, 21},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[5]=",
 CellID->2014366627]
}, Open  ]],

Cell[TextData[{
 "In FeynCalc, Passarino-Veltman coefficient functions are defined in the \
same way as in LoopTools, which is a quite common convention. If one wants to \
use a different definition, it is useful to activate the option ",
 StyleBox["GenPaVe", "ExampleText"]
}], "Notes",
 CellID->310028709],

Cell[CellGroupData[{

Cell[BoxData[
 RowBox[{"TID", "[", 
  RowBox[{"int", ",", "k", ",", 
   RowBox[{"GenPaVe", "\[Rule]", "True"}]}], "]"}]], "Input",
 CellLabel->"In[6]:=",
 CellID->1244684528],

Cell[BoxData[
 FormBox[
  RowBox[{
   RowBox[{"-", 
    RowBox[{"\[ImaginaryI]", " ", 
     SuperscriptBox["\[Pi]", "2"], " ", 
     FormBox[
      SuperscriptBox[
       FormBox[
        SubscriptBox[
         FormBox[
          FormBox["p",
           TraditionalForm],
          TraditionalForm], 
         FormBox["1",
          TraditionalForm]],
        TraditionalForm], 
       FormBox[
        FormBox[
         FormBox["\[Mu]",
          TraditionalForm],
         TraditionalForm],
        TraditionalForm]],
      TraditionalForm], " ", 
     RowBox[{"GenPaVe", "(", 
      RowBox[{
       RowBox[{"{", "1", "}"}], ",", 
       RowBox[{"(", "\[NoBreak]", GridBox[{
          {"0", "m"},
          {
           SubscriptBox["p", "1"], "0"},
          {
           SubscriptBox["p", "2"], "0"}
         },
         GridBoxAlignment->{
          "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
           "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
         GridBoxSpacings->{"Columns" -> {
             Offset[0.27999999999999997`], {
              Offset[0.7]}, 
             Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, "Rows" -> {
             Offset[0.2], {
              Offset[0.4]}, 
             Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}]}], 
      ")"}]}]}], "-", 
   RowBox[{"\[ImaginaryI]", " ", 
    SuperscriptBox["\[Pi]", "2"], " ", 
    FormBox[
     SuperscriptBox[
      FormBox[
       SubscriptBox[
        FormBox[
         FormBox["p",
          TraditionalForm],
         TraditionalForm], 
        FormBox["2",
         TraditionalForm]],
       TraditionalForm], 
      FormBox[
       FormBox[
        FormBox["\[Mu]",
         TraditionalForm],
        TraditionalForm],
       TraditionalForm]],
     TraditionalForm], " ", 
    RowBox[{"GenPaVe", "(", 
     RowBox[{
      RowBox[{"{", "2", "}"}], ",", 
      RowBox[{"(", "\[NoBreak]", GridBox[{
         {"0", "m"},
         {
          SubscriptBox["p", "1"], "0"},
         {
          SubscriptBox["p", "2"], "0"}
        },
        GridBoxAlignment->{
         "Columns" -> {{Center}}, "ColumnsIndexed" -> {}, 
          "Rows" -> {{Baseline}}, "RowsIndexed" -> {}},
        GridBoxSpacings->{"Columns" -> {
            Offset[0.27999999999999997`], {
             Offset[0.7]}, 
            Offset[0.27999999999999997`]}, "ColumnsIndexed" -> {}, 
          "Rows" -> {
            Offset[0.2], {
             Offset[0.4]}, 
            Offset[0.2]}, "RowsIndexed" -> {}}], "\[NoBreak]", ")"}]}], 
     ")"}]}]}], TraditionalForm]], "Output",
 ImageSize->{464, 49},
 ImageMargins->{{0, 0}, {0, 0}},
 ImageRegion->{{0, 1}, {0, 1}},
 CellLabel->"Out[6]=",
 CellID->2601191]
}, Open  ]]
}, Open  ]],

Cell["", "SectionFooterSpacer"]
}, Open  ]],

Cell[CellGroupData[{

Cell[TextData[{
 Cell[BoxData[
  InterpretationBox[
   StyleBox[
    GraphicsBox[{},
     BaselinePosition->Baseline,
     ImageSize->{6, 0}],
    CacheGraphics->False],
   Spacer[6]]]],
 "See Also"
}], "SeeAlsoSection",
 WholeCellGroupOpener->True,
 CellID->1255426704],

Cell[TextData[{
 StyleBox[ButtonBox["OneLoopSimplify",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/OneLoopSimplify",
  ButtonNote->"OneLoopSimplify"],
  FontFamily->"Verdana"],
 ", ",
 StyleBox[ButtonBox["TIDL",
  BaseStyle->"Link",
  ButtonData->"paclet:FeynCalc/ref/TIDL",
  ButtonNote->"TIDL"],
  FontFamily->"Verdana"],
 "."
}], "SeeAlso"]
}, Open  ]],

Cell[" ", "FooterCell"]
},
Saveable->False,
ScreenStyleEnvironment->"Working",
WindowSize->{725, 750},
WindowMargins->{{-10, Automatic}, {Automatic, -8}},
WindowTitle->"TID",
TaggingRules->{
 "ModificationHighlight" -> False, "ColorType" -> "SymbolColor", "LinkTrails" -> 
  GridBox[{{
      RowBox[{
        ButtonBox[
        "FeynCalc", ButtonData -> "paclet:FeynCalc/guide/FeynCalc", 
         BaseStyle -> {"Link", "DockedLinkTrail"}]}]}}, ColumnAlignments -> 
    Left], "HasOptions" -> False, "ExampleCounter" -> 1, "NeedPlatMsgIn" -> 
  None, "RootCaptions" -> "", 
  "Metadata" -> {
   "built" -> "{2020, 6, 20, 19, 11, 50.292695}", 
    "history" -> {"9.0", "", "", ""}, "context" -> "FeynCalc`", 
    "keywords" -> {}, "specialkeywords" -> {}, 
    "tutorialcollectionlinks" -> {}, "index" -> True, "label" -> 
    "Feyn Calc Symbol", "language" -> "en", "paclet" -> "FeynCalc", "status" -> 
    "None", "summary" -> 
    "TID[amp, q] performs tensor decomposition of 1-loop integrals with loop \
momentum q", "synonyms" -> {}, "tabletags" -> {}, "title" -> "TID", 
    "titlemodifier" -> "", "windowtitle" -> "TID", "type" -> "Symbol", "uri" -> 
    "FeynCalc/ref/TID"}, "SearchTextTranslated" -> ""},
CellContext->"Global`",
FrontEndVersion->"10.4 for Linux x86 (64-bit) (April 11, 2016)",
StyleDefinitions->Notebook[{
   Cell[
    StyleData[
    StyleDefinitions -> FrontEnd`FileName[{"Wolfram"}, "Reference.nb"]]], 
   Cell[
    StyleData["Input"], CellContext -> "Global`"], 
   Cell[
    StyleData["Output"], CellContext -> "Global`"]}, Visible -> False, 
  FrontEndVersion -> "10.4 for Linux x86 (64-bit) (April 11, 2016)", 
  StyleDefinitions -> "Default.nb"]
]
(* End of Notebook Content *)

(* Internal cache information *)
(*CellTagsOutline
CellTagsIndex->{
 "TID"->{
  Cell[5236, 162, 125, 4, 27, "Input",
   CellTags->"TID",
   CellID->1576573941],
  Cell[5364, 168, 1703, 37, 188, "Output",
   CellTags->"TID"],
  Cell[7762, 241, 571, 18, 45, "Input",
   CellTags->"TID",
   CellID->1762979144],
  Cell[8336, 261, 1235, 52, 66, "Output",
   CellTags->"TID",
   CellID->618277373],
  Cell[50474, 1510, 197, 6, 27, "Input",
   CellTags->"TID",
   CellID->1686437767],
  Cell[50674, 1518, 5110, 189, 66, "Output",
   CellTags->"TID",
   CellID->2009295439]},
 "PrimaryExamplesSection"->{
  Cell[7128, 212, 388, 15, 31, "PrimaryExamplesSection",
   CellTags->"PrimaryExamplesSection",
   CellID->1313542478]},
 "RasterizedOutput"->{
  Cell[10155, 342, 14866, 252, 246, "Output",
   CellTags->"RasterizedOutput",
   CellID->1847354466]}
 }
*)
(*CellTagsIndex
CellTagsIndex->{
 {"TID", 63836, 1995},
 {"PrimaryExamplesSection", 64356, 2013},
 {"RasterizedOutput", 64500, 2017}
 }
*)
(*NotebookFileOutline
Notebook[{
Cell[575, 21, 3099, 77, 53, "AnchorBarGrid",
 CellID->1],
Cell[3677, 100, 280, 11, 45, "ObjectNameGrid"],
Cell[CellGroupData[{
Cell[3982, 115, 432, 13, 85, "Usage",
 CellID->982511436],
Cell[CellGroupData[{
Cell[4439, 132, 738, 24, 31, "NotesSection",
 CellGroupingRules->{"SectionGrouping", 50},
 CellID->966192456],
Cell[5180, 158, 31, 0, 14, "SectionHeaderSpacer"],
Cell[CellGroupData[{
Cell[5236, 162, 125, 4, 27, "Input",
 CellTags->"TID",
 CellID->1576573941],
Cell[5364, 168, 1703, 37, 188, "Output",
 CellTags->"TID"]
}, Open  ]]
}, Closed]]
}, Open  ]],
Cell[CellGroupData[{
Cell[7128, 212, 388, 15, 31, "PrimaryExamplesSection",
 CellTags->"PrimaryExamplesSection",
 CellID->1313542478],
Cell[CellGroupData[{
Cell[7541, 231, 196, 6, 26, "ExampleSection",
 CellID->1811038592],
Cell[CellGroupData[{
Cell[7762, 241, 571, 18, 45, "Input",
 CellTags->"TID",
 CellID->1762979144],
Cell[8336, 261, 1235, 52, 66, "Output",
 CellTags->"TID",
 CellID->618277373]
}, Open  ]],
Cell[9586, 316, 417, 16, 49, "Notes",
 CellID->538152640],
Cell[CellGroupData[{
Cell[10028, 336, 124, 4, 27, "Input",
 CellID->972857906],
Cell[10155, 342, 14866, 252, 246, "Output",
 CellTags->"RasterizedOutput",
 CellID->1847354466]
}, Open  ]],
Cell[25036, 597, 174, 5, 32, "Notes",
 CellID->1396066519],
Cell[CellGroupData[{
Cell[25235, 606, 173, 5, 27, "Input",
 CellID->1927433685],
Cell[25411, 613, 24828, 885, 248, "Output",
 CellID->1959355442]
}, Open  ]],
Cell[50254, 1501, 195, 5, 48, "Notes",
 CellID->709228680],
Cell[CellGroupData[{
Cell[50474, 1510, 197, 6, 27, "Input",
 CellTags->"TID",
 CellID->1686437767],
Cell[50674, 1518, 5110, 189, 66, "Output",
 CellTags->"TID",
 CellID->2009295439]
}, Open  ]],
Cell[55799, 1710, 157, 4, 48, "Notes",
 CellID->933246479],
Cell[CellGroupData[{
Cell[55981, 1718, 746, 27, 96, "Input",
 CellID->1842388488],
Cell[56730, 1747, 1363, 53, 42, "Output",
 CellID->2014366627]
}, Open  ]],
Cell[58108, 1803, 307, 6, 66, "Notes",
 CellID->310028709],
Cell[CellGroupData[{
Cell[58440, 1813, 174, 5, 27, "Input",
 CellID->1244684528],
Cell[58617, 1820, 2693, 91, 70, "Output",
 CellID->2601191]
}, Open  ]]
}, Open  ]],
Cell[61337, 1915, 31, 0, 29, "SectionFooterSpacer"]
}, Open  ]],
Cell[CellGroupData[{
Cell[61405, 1920, 270, 12, 31, "SeeAlsoSection",
 CellID->1255426704],
Cell[61678, 1934, 355, 13, 56, "SeeAlso"]
}, Open  ]],
Cell[62048, 1950, 23, 0, 41, "FooterCell"]
}
]
*)

(* End of internal cache information *)

